Algebraic structure of the gradient expansion in linearized classical hydrodynamics

Grozdanov, Sašo (author), Vrbica, Mile (author)

In this work, we systematically treat the ambiguities that generically arise in the gradient expansion of any hydrodynamic theory. While these ambiguities do not affect the physical content of the equations, they induce two types of transformations in the space of transport coefficients. The first type is known as the “frame” transformations, and amounts to field redefinitions. The second type, which we introduce and formalize here, we term the “on-shell” transformations. This identifies equivalence classes of hydrodynamic theories that provide an equally valid low-energy description of the underlying microscopic theory. We show that in any (classical) theory of hydrodynamics (at arbitrary order in derivatives), the action of such transformations on the dispersion relations and two-point correlation functions is universal. We explicitly construct invariants which can then be matched to a microscopic theory. Among them are, expectedly, the low-momentum expansions of the hydrodynamic modes. The (unphysical) gapped modes can, however, be added or removed at will. Finally, we show that such transformations assign a nilpotent Lie group to every hydrodynamic theory, and discuss the related algebraic properties underlying classical hydrodynamics.

• Language: English
• Keywords: hydrodynamics, linear response theory, heavy-ion collisions
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: Str. 065006-1-065006-21
• Numbering: Vol. 113, iss. 6
• PID: 20.500.12556/RUL-180495
• UDC: 53
• ISSN on article: 2470-0010
• DOI: 10.1103/hkzq-b2ph
• COBISS.SI-ID: 271162371
• Publication date in RUL: 10.03.2026

Record is a part of a journal

• Title: Physical review
• Shortened title: Phys. rev., D
• Publisher: American Physical Society
• ISSN: 2470-0010
• COBISS.SI-ID: 29757223

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: hidrodinamika, teorija linearnega odziva, trki težkih ionov